Time of arrival estimation is the estimation of the travel time of a radio signal from a single transmitter to a remote single receiver. The travel time may be expressed in units of time or in units of distance, as the distance between the transmitter and the receiver can be easily calculated by multiplying the time of arrival times the known speed of the radio wave.
As shown in FIG. 1, a difficulty in the estimation of time of arrival arises from the fact that the radio wave has multiple paths from the transmitter 10 to the receiver 12. The first path 14 is the direct path from the transmitter to the receiver, and is the path that TOA estimation seeks to identify. However, the shape of a waveform generated by the receiver 12 in response to the reception of the radio signal is a combined waveform which includes noise, and a sum of the first arriving waveform (corresponding to the first path 14) with a multitude of waveforms corresponding to other paths (for examples, 16, 18, and 20) which are received by the receiver 12 at later times. Each path is filtered to a desired bandwidth as the reference waveform does not exist outside this bandwidth.
As seen in FIG. 2, the bandwidth filtering causes each waveform to have early side lobes and late side lobes. The early side lobes interfere with waveforms corresponding to preceding (shorter) paths and the late side lobes interfere with waveforms corresponding to subsequent (longer) paths (echoes or multipath). In FIG. 2, the radio wave pulse (tap) 22 which has travelled via the first path 14 and has arrived at a time τ0 has a first waveform 24 generated by the bandwidth filtering. The first waveform 24 has early side lobes 26 and late side lobes 28. Similarly, the second waveform 30 generated after bandwidth filtering the second received radio wave pulse 32 (which as travelled the second path 16) has second early lobes 34 and second late lobes 36.
Commonly the impulse response of bandwidth filter to each pulse has a sinc or similar low-pass waveform in the time domain, as seen by the shapes of the waveforms in FIG. 2. The combined waveform that is received by the receiver, therefore has a shape which includes a main lobe sided by early and late lobes. Two combined waveforms obtained by bandwidth filtering output responses of two antennas radio signals are shown in FIGS. 3 and 4. The waveforms 40 and 42 are generated by bandwidth filtering the radio wave (a plurality of pulses) as received by two respective antennas. The waveforms 40 and 42 are very different from the waveform 44 corresponding to the reference waveforms (which is the filtered transmitted waveform, i.e. the multipath waveform that is transmitted by the transmitter and filtered by the prior art filter). It is therefore very difficult to use simple signal processing to find the exact time of arrival by comparing the reference waveform 34 to the filtered waveforms.
Some techniques for extracting the time of arrival from such waveforms are known. However, such techniques are either simple to process and inaccurate or, like the Maximum Likelihood (ML) algorithm, accurate but very processing intensive, and therefore expensive.